Sculptural Imaging With Optical Tiles

ABSTRACT

The invention relates to structures for representing images by directing light at a viewer. In order to represent an image, a structure is provided comprising a plurality of tile elements ( 22 ) which, when illuminated by a light source, each direct an amount of light toward an observer at a viewing location dependent on their orientation angles. The orientation angles of each tile element ( 22 ) may be selected based on a visual characteristic of a corresponding pixel of the image, such that the observer sees a representation of that image created by the varying amount of light directed to the viewing location by the tile elements ( 22 ).

REFERENCE TO RELATED APPLICATION

This application claims priority from U.S. provisional patentapplication No. 60/582,055.

TECHNICAL FIELD

The invention relates to structures for representing images, andparticularly to structures comprising a plurality of tile elements whichreflect or refract light.

BACKGROUND

Images are often represented by applying paint or ink to a twodimensional surface. Displays having such images may be readilyproduced, but are not visually dynamic.

Artist Daniel Rozin developed an apparatus for representing images knownas the “Wooden Mirror”, which is described athttp://fargo.itp.tsoa.nyu.edu/˜danny/mirror.html. The Wooden Mirrorcomprises a plurality of pieces of wood, each of which is connected to aservo motor and can be tilted about thirty degrees up and down. If theWooden Mirror is lit from above the wood pieces which are tilted upwardsappear brighter and wood pieces which are tilted downward appear darker.

Texas Instruments™ Incorporated has developed Digital Light Processing™technology which employs digital micro-mirror devices (DMDs). Asdisclosed in U.S. Pat. No. 6,857,751 to Penn et al., a DMD “is anelectromechanical device comprising an array of thousands of tiltingmirrors. Each mirror may tilt plus or minus ten degrees for the active“on” state or “off” state. To permit the mirrors to tilt, each mirror isattached to one or more hinges mounted on support posts, and spaced bymeans of an air gap over underlying control circuitry.”

The foregoing examples of the related art and limitations relatedthereto are intended to be illustrative and not exclusive. Otherlimitations of the related art will become apparent to those of skill inthe art upon a reading of the specification and a study of the drawings.

SUMMARY OF THE INVENTION

The following embodiments and aspects thereof are described andillustrated in conjunction with systems, tools and methods which aremeant to be exemplary and illustrative, not limiting in scope. Invarious embodiments, one or more of the above-described problems havebeen reduced or eliminated, while other embodiments are directed toother improvements.

One aspect of the invention provides a structure for representing animage having a plurality of pixels. The structure comprises a pluralityof tile elements held in a fixed relationship to one another. Each ofthe tile elements comprises a generally planar surface inclined at aninclination angle with respect to a reference plane. Each of the tileelements corresponds to at least one pixel of the image and has anorientation angle with respect to a reference direction. The orientationangle defined between projections, on the reference plane, of a linenormal to the generally planar surface, and a line parallel to thereference direction. The orientation angle is determined by acharacteristic of the corresponding at least one pixel.

Another aspect of the invention provides a structure for representing animage having a plurality of pixels. The structure comprises a pluralityof tile elements held in a controlled relationship to one another. Eachof the tile elements comprises a generally planar surface inclined at aninclination angle with respect to a reference plane. Each of the tileelements corresponds to at least one pixel of the image and has anorientation angle with respect to a reference direction. The orientationangle defined between projections, on the reference plane, of a linenormal to the generally planar surface, and a line parallel to thereference direction. The orientation angle is determined by acharacteristic of the corresponding at least one pixel. The structurealso comprises a plurality of actuators for dynamically varying theorientation angles of the tile elements under control of a controlsystem. Each actuator is coupled to one of the tile elements such thateach tile element is moveable to have any one of a plurality ofdifferent orientation angles.

Another aspect of the invention comprises a method of representing animage having a plurality of pixels. The method comprises forming aplurality of tile elements held in a controlled relationship to oneanother, each of the plurality of tile elements corresponding to atleast one of the plurality of pixels and having a generally planarsurface, determining an incident light direction, and, orienting eachtile element such that the generally planar surface is inclined at aninclination angle with respect to a reference plane, and such that aprojection of a line normal to the generally planar surface on thereference plane and a projection of the incident light direction on thereference plane define an orientation angle. The orientation angle ofeach tile element is determined by a characteristic of the correspondingat least one pixel.

In addition to the exemplary aspects and embodiments described above,further aspects and embodiments will become apparent by reference to thedrawings and by study of the following detailed descriptions.

BRIEF DESCRIPTION OF THE DRAWINGS

Exemplary embodiments are illustrated in referenced figures of thedrawings. It is intended that the embodiments and figures disclosedherein are to be considered illustrative rather than restrictive. Indrawings which illustrate non-limiting embodiments of the invention:

FIG. 1 schematically depicts a structure for representing an imageaccording to one embodiment of the invention;

FIG. 2 is a sectional view taken along line A-A of FIG. 1;

FIGS. 3 to 5 show the structure of FIG. 1 with light incident thereonfrom different directions;

FIGS. 6A to 6C show a structure according to another embodiment of theinvention from different viewing angles;

FIG. 7 schematically depicts a translucent structure coupled to ahousing having a light source therein according to one embodiment of theinvention;

FIG. 7A is a sectional view taken along line A-A of FIG. 7;

FIG. 8 shows an apparatus for making a structure for representing animage according to another embodiment of the invention;

FIG. 9 shows one of the recesses of the apparatus of FIG. 8;

FIG. 10 is a flowchart illustrating a method of controlling theapparatus of FIG. 8;

FIG. 11 shows a single tile element of a structure for representing animage according to another embodiment of the invention;

FIG. 12 is an exploded view of the tile element of FIG. 11;

FIG. 13 shows a structure for representing an image according to anotherembodiment of the invention;

FIG. 14 shows a single tile element attached to an individual substrateelement according to another embodiment of the invention;

FIG. 15 shows a structure for representing an image according to anotherembodiment of the invention;

FIG. 16 shows a structure with active tile elements for representingdynamic images according to one embodiment of the invention;

FIG. 17 shows an active tile element according to one embodiment of theinvention;

FIG. 18 shows an active tile element according to another embodiment ofthe invention;

FIG. 19 is a rear view of the active tile element of FIG. 18;

FIG. 20 is a bottom view of the active tile element of FIG. 18;

FIG. 21 shows an active tile element according to another embodiment ofthe invention;

FIG. 22 is a sectional view taken along line A-A of FIG. 21;

FIG. 23 shows an active tile element according to another embodiment ofthe invention;

FIG. 24 is a bottom perspective view of the active tile element of FIG.23;

FIG. 25 is a flowchart illustrating a method of controlling thestructure with active tile elements of FIG. 16;

FIG. 26 shows a tile element having a plurality of smaller tile elementsformed thereon according to another embodiment of the invention;

FIG. 27 is a front view of the tile element of FIG. 26;

FIG. 28 shows a three dimensional array of tile elements according toanother embodiment of the invention; and

FIG. 29 illustrates the geometry of a tile element with respect to areference plane.

DESCRIPTION

Throughout the following description, specific details are set forth inorder to provide a more thorough understanding of the invention.However, the invention may be practiced without these particulars. Inother instances, well known elements have not been shown or described indetail to avoid unnecessarily obscuring the invention. Accordingly, thespecification and drawings are to be regarded in an illustrative, ratherthan a restrictive, sense.

The invention provides structures for representing images. Structuresaccording to the invention comprise a plurality of tile elements which,when illuminated by a light source, each direct an amount of lighttoward an observer at a viewing location dependent on the orientationangles of respective tile elements relative to the light source. Theorientation angles of each tile element may be selected based on acharacteristic of a corresponding pixel of an image, such that theobserver sees a representation of that image created by the varyingamount of light directed to the viewing location by the tile elements.

In some embodiments, the invention provides a structure for reflectinglight incident on a front side thereof. The structure comprises asubstrate having plurality of tile elements coupled thereto. The tileelements may each comprise a reflective tile having a generally planarsurface inclined at an acute angle with respect to the substrate. Eachtile element may correspond to one of a plurality of pixels of an image.The tile elements may be oriented with respect to the light incident onthe structure such that tile elements which correspond to brightest onesof the image pixels reflect a maximum amount of light toward the viewinglocation, and tile elements which correspond to least bright ones of theimage pixels reflect a minimum amount of light toward the viewinglocation.

FIG. 1 shows a structure 10 according to one embodiment of theinvention. FIG. 2 is a sectional view of structure 10 taken along lineA-A of FIG. 1. Structure 10 displays an image having three regions 12,14 and 16, and is illuminated by light incident on the front ofstructure 10 in a direction indicated by arrows 18. In the FIG. 1example, arrows 18 are pointing down, meaning that light is incident onstructure 10 from a position generally in front of and above structure10.

Structure 10 comprises a substrate 20 having a plurality of tileelements 22 coupled thereto. Tile elements 22 may be constructed from amaterial which reflects light. In the embodiment of FIGS. 1 and 2, tileelements 22 comprise cylindrical protrusions 24, each having a shearedend surface 26 inclined at an angle with respect to a reference plane(referred to as the “inclination angle”). In the embodiment of FIGS. 1and 2, the reference plane is parallel to the surface of substrate 20,and surfaces 26 all have inclination angles of about 30 degrees.However, it is to be understood that surfaces 26 could have differentinclination angles, and not all surfaces 26 need to have the sameinclination angle.

Each tile element 22 is oriented such that a projection of a line normalto surface 26 on the reference plane (i.e., the surface of substrate 20)forms an angle with a projection of line parallel to a referencedirection (i.e., the direction from which light is incident on structure10) on the reference plane. This angle is referred to herein as the“orientation angle” of each tile element 22. FIG. 29 illustrates thegeometry of a tile element having a surface S, an inclination angle θand an orientation angle Φ with respect to a reference plane P andincident light L. The line normal to surface S is identified byreference character N.

Surfaces 26 reflect light in an amount which varies depending on theorientation angles of tile elements 22. In the embodiment of FIGS. 1 and2, surfaces 26 in region 12 face upwardly (i.e., the projections of theline normal to surface 26 and the direction from which light is incidenton structure 10 on the reference plane are parallel and pointing in thesame direction, which corresponds to an orientation angle of zerodegrees), surfaces 26 in region 14 face to the right (i.e., anorientation angle of ninety degrees), and surfaces in region 16 facedownwardly (i.e., an orientation angle of one hundred eighty degrees).Thus, tile elements 22 in region 12 appear brightest, because theassociated surfaces 26 reflect the most light. Tile elements 22 inregion 14 appear intermediately bright, because the associated surfaces26 reflect an intermediate amount of light. Tile elements in region 16appear the least bright, because the associated surfaces 26 reflect theleast light.

As can be seen in FIGS. 3, 4 and 5, changing the direction from whichlight is incident on structure 10 changes the appearance of structure10. In FIG. 3, light is incident on structure 10 from a positiongenerally in front of and below structure 10, and region 12 is the leastbright and region 16 is the most bright (i.e., structure 10 appears todisplay a negative of the image shown in FIG. 1). This is because theorientation angle of each tile element 22 in region 12 is one hundredeighty degrees relative to the direction from which light is incident onstructure 10 and the orientation angle of each tile element 22 in region16 is zero degrees relative to the direction from which light isincident on structure 10 in FIG. 3.

In FIG. 4, light is incident on structure 10 from a position generallyin front of and to the left of structure 10, and regions 12 and 16 areintermediately bright, and region 14 is the least bright. This isbecause the orientation angle of each tile element 22 in regions 12 and16 is ninety degrees relative to the direction from which light isincident on structure 10, and the orientation angle of each tile element22 in region 14 is one hundred eighty degrees relative to the directionfrom which light is incident on structure 10 in FIG. 4.

In FIG. 5, light is incident on structure 10 from a position generallyin front of and to the right of structure 10, and regions 12 and 16 areintermediately bright, and region 14 is the most bright (i.e., structure10 appears to display a negative of the image shown in FIG. 4). This isbecause the orientation angle of each tile element 22 in regions 12 and16 is ninety degrees relative to the direction from which light isincident on structure 10, and the orientation angle of each tile element22 in region 14 is zero degrees relative to the direction from whichlight is incident on structure 10 in FIG. 4.

Structure 10 may be used to represent an image having the sameresolution as structure 10 (i.e., the same number of pixels as thenumber of tile elements 22 of structure 10) by selecting the inclinationand orientation angles of each tile element 22 based on a characteristicof a corresponding pixel of the image. For example, the incline andorientation angles of each tile element 22 may be selected based on thebrightness of the corresponding pixel. Also, images having a differentresolution than structure 10 may be converted into corresponding imageshaving the same resolution as structure 10 by known conversion methods.Alternatively, each tile element 22 could correspond to a plurality ofpixels of the image, of a plurality of tile elements 22 could correspondto a single pixel of the image.

As noted above, images represented by structures such as structure 10may appear different when illuminated by light from differentdirections. Also, such images may appear different when viewed fromdifferent viewing locations, since the relative amount of surface areaof each tile element 22 facing the viewer depends on the position of theviewer. Even if a structure such as structure 10 is illuminated from adirection perpendicular to the reference plane, a viewer may be able tosee the image represented by structure 10 from certain viewing locationsdue to the relative amount of surface area of tile elements 22 facingtoward the viewer.

For example, FIGS. 6A to 6C show a structure 28 according to anotherembodiment of the invention from different viewing angles. Structure 28comprises a generally circular substrate having tile elements in theform of cylindrical protrusions which represent an image of the MonaLisa. FIG. 6A shows structure 28 from a first acute viewing angle. FIG.6B shows structure 28 from a second acute viewing angle. FIG. 6C showsstructure 28 from a perpendicular viewing angle. It can be seen that theluminance values of the image represented by structure 28 are differentfrom different viewing angles, due to differences in the relative amountof surface area of the tile elements facing the observer.

As another example, referring to FIGS. 1 and 2, region 14 would appearbrighter when viewed from the right (i.e., from the direction in whichsurfaces 26 in region 14 are facing) and darker when viewed from theleft (i.e., from the direction opposite to the direction in whichsurfaces 26 in region 14 are facing). Thus, when an observer passes by astructure such as structure 10, the observer is presented with an imagehaving luminance characteristics which change as the observer moves,producing a striking visual effect.

Structures such as structure 10 may be illuminated with light fromdifferent light sources incident on the structures at different angles.The different light sources may emit different colours of light, suchthat the colours appear to mix together when viewed by an observer.

The visual effect produced by a structure such as structure 10 may beenhanced by applying coatings to substrate 20 and/or surfaces 26. Forexample, a flat or matte white coating may be applied to surfaces 26,and a dark coating may be applied to substrate 20. Alternatively,surfaces 26 may be covered with an iridescent or fluorescent coating.Other coatings which enhance, augment or alter reflectivity may also beused to cover substrate 20 and/or surfaces 26, and substrate 20 and/orsurfaces 26 may themselves be constructed from materials which enhance,augment or alter reflectivity.

In another embodiment, a substantially non-reflective coating may beapplied to substrate 20, and a substantially reflective coating may beapplied to surfaces 26. In such an embodiment, structure 10 may bepositioned to reflect light from a light source to project the imageonto a screen or the like. Structure 10 may alternatively oradditionally be positioned such that surfaces 26 reflect colour from thesurrounding environment to the observer.

Structures according to some embodiments of the invention may beconstructed from translucent material and viewed from the back (i.e.,the side opposite the one from which light is incident thereon). FIGS. 7and 7A show an example of such a structure 30 used to represent an imageI. Structure 30 is coupled to a housing 32 having a light source 34therein. Structure 30 is constructed from a translucent material suchas, for example, glass or acrylic. Areas of substrate 20 between tileelements may optionally be made opaque or covered with an opaquecoating. In some embodiments it may be desirable to use a translucentmaterial having an index of refraction of between 1 and 1.3. In otherembodiments, translucent materials having higher indices of refractionmay be selected.

Light from light source 34 is incident on surfaces 26 of tile elements22 of structure 30, and is refracted by structure 30 to represent imageI. Each tile element 22 corresponds to at least one pixel of image I.The orientation angle of each tile element 22 is selected such thatlight is incident on surface 26 at an angle of incidence which dependson characteristics (e.g., brightness) of the corresponding pixel ofimage I. For example, tile elements 22 which correspond to the brightestpixels of image I have an orientation angle of zero degrees (i.e.,surfaces 26 face toward light source 34), and are collectively indicatedby reference numeral 36 in FIG. 7A. Also, the inclination angles of tileelements 22 may vary depending on the distance from light source 34,with surfaces 26 farther away from light source 34 having a greaterinclination angle than surfaces 26 closer to light source 34, such thatthe angle of incidence of light from light source 34 is relativelyconstant for all tile elements having an orientation angle of zerodegrees. Tile elements 22 which correspond to the least bright pixels ofimage I have an orientation angle of 180 degrees (i.e., surfaces 26 faceaway from light source 34), and are collectively indicated by referencenumeral 38 in FIG. 7A.

Structures such as structure 30 may be illuminated with light fromdifferent light sources incident on the structures at different angles.The different light sources may emit different colours of light, suchthat the colours appear to mix together when viewed by an observer.

Structure 10 or structure 30 may be constructed, for example, bymachining a block of material to create cylindrical protrusions 24 andsubstrate 20. Then tile elements 22 may be formed by cutting cylindricalprotrusions 24 according to the inclination and orientation anglesassigned to tile elements 22 based on characteristics of the pixels ofthe image to be represented. Alternatively, structure 10 or structure 30may be constructed by attaching pre-formed tile elements 22 to asubstrate. In another example, structure 10 or structure 30 may beformed by constructing a mold and inserting a moldable material into themold and allowing it to harden in the shape of structure 10 or structure30.

FIG. 8 shows an apparatus 40 for forming a structure by molding, such asfor example structure 10 or structure 30. Apparatus 40 comprises a base42 and a wall 44 extending upwardly therefrom to define a volume 46.Base 42 has a plurality of recesses 48 therein. A moldable material maybe introduced into volume 46 and allowed to harden to form a surfacewherein tile elements 22 comprise protrusions 24 corresponding torecesses 48. The moldable material may be, for example, poured into thevolume, pressed into the volume, or sucked into the volume by creating areduced pressure in the volume.

FIG. 9 shows one of recesses 48 of FIG. 10. Recess 48 has a cylindricalplug 50 therein. Cylindrical plug 50 may be rotated as indicated byarrows 52 to select the orientation angle of tile element 22 formed inrecess 48. The orientation of cylindrical plug 50 may be controlled by acontrol system 54. Control system 54 may be used to control theorientation of cylindrical plugs 50 in all of recesses 48 of FIG. 8.

FIG. 10 is a flow chart illustrating a method 200 which may be carriedout by control system 54. At block 202 control system 54 receives animage to be represented by a structure to be formed with apparatus 40,and also receives information about the direction from which light willbe incident of the structure to be formed. At block 204 control system54 determines if the resolution of the image received at block 202 needsto be adjusted (i.e., if the image has a different number of pixels fromthe number of recesses 48). If the resolution needs to be adjusted(block 204 YES output) method 200 proceeds to block 206, where controlsystem 54 adjusts the resolution of the image to match that of apparatus40. If the image has a higher resolution than apparatus 40, theresolution of the image may be adjusted by grouping a plurality ofpixels of the image together and calculating a single adjusted pixelfrom the plurality of pixels, such that there is one adjusted pixel foreach recess 48. If the image has a lower resolution than apparatus 40,the resolution of the image may be adjusted by converting each pixel ofthe image into a plurality of adjusted pixels, such that there is oneadjusted pixel for each recess 48.

If the resolution of the image does not need to be adjusted (block 204NO output), or after the image resolution has been adjusted at block206, method 200 proceeds to block 208 where control system 54 assignsorientation angles to the tile elements to be formed in recesses 48based on characteristics of the corresponding pixels (or adjustedpixels) of the image. At block 210 control system 54 rotates cylindricalplugs 50 to orientations corresponding to the orientation anglesassigned at block 208, and apparatus 40 is ready to receive the moldablematerial in volume 46. Apparatus 40 of FIG. 8 may be used, for example,in conjunction with thermo-plastic embossing or thermo-plastic moldingtechniques to introduce the moldable material into volume 46.

FIGS. 11 and 12 show a tile element 55 according to another embodimentof the invention. Tile element 55 comprises a sheared cylinder 56 havinga circumferentially toothed base 57. Toothed base 57 is received in anannular member 58 having correspondingly shaped teeth on the insidecircumference thereof. Annular member 58 is inserted into a hole 59 inthe substrate. The orientation angle of tile element 55 may be adjustedto select any one of a plurality of discrete values by inserting base 57of sheared cylinder 56 into annular member 58 in any of one of aplurality of orientations permitted by inter-engagement of toothed base57 and member 58.

FIG. 13 shows a structure 60 according to another embodiment of theinvention. In structure 60 the substrate comprises a sheet 62, and thetile elements comprise tabs 64 formed from sheet 62 and bent at thedesired inclination and orientation angles. Structure 60 of FIG. 13 mayalso comprise graphic features (not shown). For example, sheet 62 may beprinted or treated with a thermal overlay to form an image from pigmentthereon, either before or after tabs 64 are formed from sheet.

Structures according to the invention need not necessarily comprise asubstrate, so long as the tile elements are held in a controlledrelationship to one another. Also, structures according to someembodiments of the invention could comprise a plurality of individualsubstrate elements which may be connected to one another.

FIG. 14 shows a single tile element 66 comprising a tab 64 formed froman individual substrate element 68. A plurality of tile elements 66 maybe combined by joining their respective substrate elements 68 to form astructure such as structure 60 of FIG. 13.

FIG. 15 shows a structure 70 according to another embodiment of theinvention. In structure 70 the substrate comprises an optical medium 72,and the tile elements comprise regions 74 of interrupted transparencysuspended in medium 72. Medium 72 may comprise a transparent materialsuch as glass or acrylic, for example. Regions 74 may be formed, forexample, by subsurface etching in medium 72. Alternatively, regions 74could be formed by embedding opaque or partially opaque members inmedium 72.

FIG. 16 shows a dynamic structure 80 for representing dynamic imagesaccording to one embodiment of the invention. Structure 80 comprises asubstrate 82 having a plurality of active tile elements 84 coupledthereto. Active tile elements 84 are operably connected to a controlsystem 86 such that the orientation angle of each active tile element 84can be dynamically controlled by control system 86. In some embodiments,control system 86 can also dynamically control the inclination angles ofactive tile elements 84. Control system 86 provides power and controlsignals to structure 80. In the illustrated embodiment, control system86 is connected to structure 80 by means of a cable, control system 86could alternatively communicate with structure 80 by wireless means, andstructure 80 could receive power from solar panels.

FIG. 17 shows an example active tile element 84A according to oneembodiment of the invention. Active tile element 84A comprises a shearedcylinder 88 coupled to a rotary actuator 89. Rotary actuator 89 may becoupled to substrate 82 (not shown in FIG. 17). Rotary actuator 89adjusts the orientation angle of active tile element 84A by rotatingsheared cylinder 88 under the control of control system 86 (not shown inFIG. 17).

FIGS. 18 to 20 show an example active tile element 84B according toanother embodiment of the invention. Active tile element 84B comprises aspherical section 90 positioned in a cup 92. Spherical section 90 isheld in place by retaining means 94 attached to cup 92. For example, cup92 may be a hemisphere having a radius slightly larger than the radiusof spherical section 90, and retaining means 94 may comprise anapertured sized to fit over spherical section 90. Cup 92 has three coils96 therein. Spherical section 90 has a magnet 98 therein, which maycomprise a permanent or electromagnet. Electric current is passedthrough coils 96 to create magnetic fields for adjusting the position ofmagnet 98 and therefore spherical section 90 under the control ofcontrol system 86 (not shown in FIGS. 18 to 20) to control theinclination and orientation angles of active tile element 84B.

FIGS. 21 and 22 show an example active tile element 84C according toanother embodiment of the invention. Active tile element 84C comprises aplatform 100 pivotally mounted on a hollow base 102 by means of a balljoint 104. Platform 100 has a shaft 106 attached thereto. A magnet 108is attached to the end of shaft 106 opposite platform 100. Magnet 108may comprise a permanent or electromagnet. Base 102 has three coils 109therein. Electric current is passed through coils 109 to create magneticfields for adjusting the position of magnet 108 and therefore platform100 under the control of control system 86 (not shown in FIGS. 21 and22) to control the inclination and orientation angles of active tileelement 84C.

FIGS. 23 and 24 show an example active tile element 84D according toanother embodiment of the invention. Active tile element 84D comprises aplatform 110 attached to a shaft 112. The inclination angle of activetile element 84D is fixed. Shaft 112 is rotatably coupled to a substrateelement 114 by coupling means 116. The end of shaft 112 oppositeplatform 110 is coupled to a rotary actuator 118. Rotary actuator 118rotates shaft 112 and therefore platform 110 under the control ofcontrol system 86 (not shown in FIGS. 23 and 24) to control theorientation angle of active tile element 84D.

FIG. 25 is a flowchart illustrating a method 300 carried out by controlsystem 86 of FIG. 16 for controlling active tile elements 84 ofstructure 80. At block 302 control system 86 receives an image to berepresented by structure 80. At block 304 control system 86 determinesif the resolution of the image received at block 302 needs to beadjusted (i.e., if the image has a different number of pixels from thenumber of tile elements 84). If the resolution needs to be adjusted(block 304 YES output) method 300 proceeds to block 306, where controlsystem 86 adjusts the resolution of the image to match that of structure80. If the image has a higher resolution than structure 80, theresolution of the image may be adjusted by grouping a plurality ofpixels of the image together and calculating a single adjusted pixelfrom the plurality of pixels, such that there is one adjusted pixel foreach tile element 84. If the image has a lower resolution than structure80, the resolution of the image may be adjusted by converting each pixelof the image into a plurality of adjusted pixels, such that there is oneadjusted pixel for each tile element 84.

If the resolution of the image does not need to be adjusted (block 304NO output), or after the image resolution has been adjusted at block306, method 300 proceeds to block 308 where control system 86 determinesthe direction (or directions, if structure 80 is illuminated by morethan one light source) from which light is incident on structure 80.Control system 86 may determine the direction(s) from which light isincident on structure 80 by receiving information from a light sensor.Alternatively or additionally, in situations where structure 80 islocated outside, control system 86 may be programmed to determine thedirection(s) from which light is incident on structure 80 based on thetime of day.

At block 310 control system 86 assigns orientation angles to active tileelements 84 based on characteristics of the corresponding pixels of theimage received at block 302. At block 312 control system 86 adjustsactive tile elements 84 to the orientation angles assigned at block 310,and then method returns to block 302 to receive a new image.

FIGS. 26 and 27 show a tile element 120 according to another embodimentof the invention. Tile element 120 comprises a sheared cylinder 122having a plurality of smaller tile elements 124 on a surface 126thereof. Smaller tile elements 124 may be used to represent an image onsurface 126, such as the Mona Lisa in the illustrated embodiment.

FIG. 28 shows a three dimensional array 130 according to anotherembodiment of the invention. Three dimensional array 130 comprises aplurality of tile elements 132 suspended on lines 134 such that tileelements 132 are held in a controlled relationship to one another. Lines134 are arranged in rows 136, with tile elements 132 of each row 136being used to represent a two dimensional slice of a three dimensionalimage. Tile elements 132 may have varying levels of transparency, withtile elements 132 near the middle of array 130 being the leasttransparent, and those near the edges of array 130 being the mosttransparent. Alternatively, tile elements 132 may all have the samelevel of transparency.

As will be apparent to those skilled in the art in the light of theforegoing disclosure, many alterations and modifications are possible inthe practice of this invention without departing from the spirit orscope thereof. For example:

-   In the illustrated embodiments the tile elements have circular or    elliptical surfaces, but the surfaces could have different shapes.    However, circular and elliptical surfaces provide for a smoother    looking image, particularly when the observer moves between    different viewing locations.-   In most of the illustrated embodiments the substrates are    rectangular, but the substrates could have any shape.-   In the illustrated embodiments the substrates are all generally    planar, but the substrates could be non-planar.

While a number of exemplary aspects and embodiments have been discussedabove, those of skill in the art will recognize certain modifications,permutations, additions and sub-combinations thereof. It is thereforeintended that the following appended claims and claims hereafterintroduced are interpreted to include all such modifications,permutations, additions and sub-combinations as are within their truespirit and scope.

1. A structure for representing an image having a plurality of pixels,the structure comprising: a plurality of tile elements held in a fixedrelationship to one another, each of the tile elements comprising agenerally planar surface inclined at an inclination angle with respectto a reference plane, each of the tile elements corresponding to atleast one pixel of the image and having an orientation angle withrespect to a reference direction, the orientation angle defined betweenprojections, on the reference plane, of: a line normal to the generallyplanar surface; and a line parallel to the reference direction, whereinthe orientation angle is determined by a characteristic of thecorresponding at least one pixel.
 2. A structure according to claim 1wherein the tile elements are illuminated by light from a light sourcewhich is incident on the structure from an illumination direction andthe reference direction comprises the illumination direction.
 3. Astructure according to claim 1 further comprising a substrate having asurface, wherein the plurality of pixel elements are coupled to thesubstrate surface.
 4. A structure according to claim 3 wherein each tileelement further comprises a protrusion projecting from the surface ofthe substrate.
 5. A structure according to claim 4 wherein eachprotrusion is cylindrical.
 6. A structure according to claim 3 whereinthe substrate further comprises a sheet and each tile element furthercomprises a tab formed from the sheet.
 7. A structure according to claim3 wherein the substrate comprises an optical medium and each tileelement comprises a region of interrupted transparency in the opticalmedium.
 8. A structure according to claim 3 wherein the substratefurther comprises a plurality of toothed apertures, and each tileelement further comprises a sheared cylinder having a toothed baseadapted to engage one of the toothed apertures.
 9. A structure accordingto claim 1 wherein the plurality of tile elements are linearly suspendedin one or more columns.
 10. A structure according to claim 9 wherein thecolumns are arranged to form a three dimensional array of tile elements.11. A structure according to claim 1 wherein all of the tile elementshave the same inclination angle.
 12. A structure according to claim 1wherein the orientation angle of each tile element is based on abrightness of the corresponding pixel.
 13. A structure according toclaim 1 wherein the generally planar surface of each tile element has amatte white coating.
 14. A structure according to claim 3 wherein thesurface of the substrate is substantially non-reflective and thegenerally planar surface of each tile element is substantiallyreflective.
 15. A structure according to claim 4 wherein the substrateand the protrusions are formed from a translucent material.
 16. Astructure according to claim 15 wherein the translucent material has anindex of refraction in the range of 1 to 1.3.
 17. A display apparatuscomprising a structure according to claim 15 within a housing containinga light source.
 18. A display apparatus according to claim 17 whereinthe structure coincides with a wall of the housing and the protrusionsproject into the housing, such that light from the light source isrefracted by the structure to display the image.
 19. A structureaccording to claim 3 wherein the substrate is non-planar.
 20. A methodof constructing the structure of claim 4, the method comprising:providing the substrate having the surface; forming the plurality ofprotrusions thereon extending generally perpendicularly to the surfaceof the substrate; assigning the orientation angle to each of theprotrusions based on the characteristic of the corresponding at leastone pixel; and cutting each of protrusions downwardly in a directionalong the orientation angle to form a generally planar end surfaceinclined at the acute angle with respect to the surface of thesubstrate.
 21. A method according to claim 20 wherein forming theplurality of protrusions further comprises machining the surface of thesubstrate to form a plurality of cylinders extending generallyperpendicularly from the surface of the substrate.
 22. A methodaccording to claim 20 wherein assigning the orientation angle to each ofthe protrusions further comprises determining a brightness of the atleast one corresponding pixel for each protrusion.
 23. A methodaccording to claim 22 wherein assigning the orientation angle to each ofthe protrusions further comprises determining a direction from whichlight will be incident on the protrusions and assigning a value withinthe range of −180 to +180 degrees from the incident light direction asthe orientation angle for each protrusion, wherein protrusions for whichthe at least one corresponding pixel is brightest have a value of 0degrees assigned as the orientation angle and protrusions for which theat least one corresponding pixel is least bright have a value of ±180degrees assigned as the orientation angle.
 24. A method according toclaim 23 wherein the orientation angle of each of the protrusions iscontinuously variable in the range of −180 to +180 degrees such thatarbitrarily fine variations in the brightness of the at least onecorresponding pixel may be represented by the protrusion.
 25. Anapparatus for constructing the structure of claim 5, the apparatuscomprising: a base having a plurality of recesses therein, each recesscorresponding to one to the protrusions; a wall extending upwardly fromthe base to define a volume; and a cylindrical plug in each of therecesses, the cylindrical plug connected to be controllably rotatedaccording to the orientation angle of the corresponding tile element,such that a moldable material may be introduced into the volume andallowed to harden to produce the structure.
 26. A method of using anapparatus according to claim 25 wherein the moldable material is pouredinto the volume.
 27. A method of using an apparatus according to claim25 wherein the moldable material is pressed into the volume.
 28. Amethod of using an apparatus according to claim 25 wherein the moldablematerial is sucked into the volume by creating a reduced pressure in thevolume.
 29. A method of using an apparatus according to claim 25 whereinthe moldable material is introduced into the volume by thermoplasticembossing.
 30. A method of using an apparatus according to claim 25wherein the moldable material is introduced into the volume bythermoplastic molding.
 31. A structure for representing an image havinga plurality of pixels, the structure comprising: a plurality of tileelements held in a controlled relationship to one another, each of thetile elements comprising a generally planar surface inclined at aninclination angle with respect to a reference plane, each of the tileelements corresponding to at least one pixel of the image and having anorientation angle with respect to a reference direction, the orientationangle defined between projections, on the reference plane, of: a linenormal to the generally planar surface; and a line parallel to thereference direction, wherein the orientation angle is determined by acharacteristic of the corresponding at least one pixel; and a pluralityof actuators for dynamically varying the orientation angles of the tileelements under control of a control system, each actuator being coupledto one of the tile elements such that each tile element is moveable tohave any one of a plurality of different orientation angles.
 32. Astructure according to claim 31 wherein the actuators are adapted todynamically vary both the inclination and the orientation angles of thetile elements under control of the control system.
 33. A structureaccording to claim 31 wherein each tile element further comprises aprotrusion projecting from a surface of a substrate, and wherein eachactuator further comprises a rotary actuator connected to rotate acorresponding one of the protrusions.
 34. A structure according to claim31 wherein each tile element further comprises a platform coupled to ashaft, and wherein each actuator further comprises a rotary actuatorconnected to rotate a corresponding one of the shafts.
 35. A structureaccording to claim 32 wherein each tile element further comprises aspherical section held in a cup by retaining means, the sphericalsection having a magnet therein, and wherein each actuator furthercomprises at least three coils positioned in the cup and connected toreceive current to generate magnetic fields for controlling theinclination and orientation angles of a corresponding one of the tileelements.
 36. A structure according to claim 32 wherein each tileelement further comprises a platform pivotally coupled to a base, theplatform having a shaft extending therefrom into a cavity in the base,the shaft having a magnet at an end thereof opposite the platform, andwherein each actuator further comprises at least three coils positionedin the base and connected to receive current to generate magnetic fieldsfor controlling the inclination and orientation angles of acorresponding one of the tile elements.
 37. A method of representing animage having a plurality of pixels, the method comprising: forming aplurality of tile elements held in a controlled relationship to oneanother, each of the plurality of tile elements corresponding to atleast one of the plurality of pixels and having a generally planarsurface; determining an incident light direction; and orienting eachtile element such that the generally planar surface is inclined at aninclination angle with respect to a reference plane, and such that aprojection of a line normal to the generally planar surface on thereference plane and a projection of the incident light direction on thereference plane define an orientation angle, wherein the orientationangle of each tile element is determined by a characteristic of thecorresponding at least one pixel.
 38. A method according to claim 37further comprising determining a brightness of the at least onecorresponding pixel for each tile element.
 39. A method according toclaim 38 further comprising assigning a value within the range of −180to +180 degrees as the orientation angle for each tile element, whereintile elements for which the at least one corresponding pixel isbrightest have a value of 0 degrees assigned as the orientation angleand tile elements for which the at least one corresponding pixel isleast bright have a value of −180 degrees assigned as the orientationangle.
 40. A method according to claim 39 wherein the orientation angleof each tile element is continuously variable in the range of −180 to+180 degrees such that arbitrarily fine variations in the brightness ofthe at least one corresponding pixel may be represented by the tileelement.